State whether the given set is finite or infinite.
Set of all odd intergers.

Answer

To determine whether the set of all odd integers is finite or infinite, we can follow these steps:

### Step 1: Define the Set
The set of all odd integers can be represented as:
\[ \{1, 3, 5, 7, 9, \ldots\} \]
This set includes all integers that are not divisible by 2.

**Hint:** Think about what defines an odd integer and how they are arranged on the number line.

### Step 2: Identify the Pattern
Notice that the odd integers continue indefinitely. They can be expressed in a general form:
\[ 2n + 1 \]
where \( n \) is any integer (0, 1, 2, 3, ...). This means for every integer \( n \), there is a corresponding odd integer.

**Hint:** Consider how you can generate odd integers using a formula based on integers.

### Step 3: Analyze the Set
Since there is no largest odd integer (you can always add 2 to get the next odd integer), the set does not have an endpoint. Therefore, it continues infinitely in both the positive and negative directions.

**Hint:** Think about whether you can list all the elements of the set without stopping.

### Step 4: Conclusion
Since the set of all odd integers has no limit and continues indefinitely, we conclude that the set is infinite.

**Final Answer:** The set of all odd integers is infinite.

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